find all critical numbers of f(x) = (x - 1)^2 * (x - 2)^3

Question

anonymous · Answer

starting with finding the derivative, I get f'(x) = 2(x-1)(x-2)^3 + 3(x-2)^2 * (x - 1)^2

misty1212 · Answer

HI!!

misty1212 · Answer

by some total miracle this actually factors as $$(x-2)^2 (x-1) (5 x-7)$$ so the critical numbers are real easy to find

misty1212 · Answer

actually it is not really a miracle since you can factor out the common factor of $(x-2)^2(x-1)$ and see what you have left

anonymous · Answer

now, I would find when the derivative would equal zero, can someone walk me through this?

anonymous · Answer

set each factor equal to zero and solve
you do it in your head mostly

anonymous · Answer

thanks to both of you for your help.  there are connection issues here, and I was stuck as factoring as the first step.

anonymous · Answer

so, got 1,2,7/5